Resonant-state expansion of the Green's function of open quantum systems

Our series of recent work on the transmission coefficient of open quantum systems in one dimension will be reviewed. The transmission coefficient is equivalent to the conductance of a quantum dot connected to leads of quantum wires. We will show that the transmission coefficient is given by a sum over all discrete eigenstates without a background integral. An apparent "background" is in fact not a background but generated by tails of various resonance peaks. By using the expression, we will show that the Fano asymmetry of a resonance peak is caused by the interference between various discrete eigenstates. In particular, an unstable resonance can strongly skew the peak of a nearby resonance.Comment: 7 pages, 7 figures. Submitted to International Journal of Theoretical Physics as an article in the Proceedings for PHHQP 2010 (http://www.math.zju.edu.cn/wjd/

Pseudo-time Schroedinger equation with absorbing potential for quantum scattering calculations

The Schroedinger equation with an energy-dependent complex absorbing potential, associated with a scattering system, can be reduced for a special choice of the energy-dependence to a harmonic inversion problem of a discrete pseudo-time correlation function. An efficient formula for Green's function matrix elements is also derived. Since the exact propagation up to time 2t can be done with only t real matrix-vector products, this gives an unprecedently efficient scheme for accurate calculations of quantum spectra for possibly very large systems.Comment: 9 page

Time Asymmetric Quantum Physics

Mathematical and phenomenological arguments in favor of asymmetric time evolution of micro-physical states are presented.Comment: Tex file with 2 figure

The Hyperspherical Four-Fermion Problem

The problem of a few interacting fermions in quantum physics has sparked intense interest, particularly in recent years owing to connections with the behavior of superconductors, fermionic superfluids, and finite nuclei. This review addresses recent developments in the theoretical description of four fermions having finite-range interactions, stressing insights that have emerged from a hyperspherical coordinate perspective. The subject is complicated, so we have included many detailed formulas that will hopefully make these methods accessible to others interested in using them. The universality regime, where the dominant length scale in the problem is the two-body scattering length, is particularly stressed, including its implications for the famous BCS-BEC crossover problem Derivations and relevant formulas are also included for the calculation of challenging few-body processes such as recombination.Comment: 66 pages, 33 figure

Regenerative pulsations in semiconductor etalon due to competition between carrier generation and heating effects on band filling

Competition between carrier concentration and effective temperature effects on the dielectric function of a degenerate semiconductor in a spectral range near its fundamental absorption edge is suggested as a mechanism for regenerative pulsations in a stationary pumped optical etalon. The origin of self-pulsations is similar to that in a bistable etalon with competing concentration and thermal optical nonlinearities, but, due to its purely electronic nature, the proposed mechanism provides a way for a much higher repetition frequency, probably in the GHz range. The model of the phenomenon and modeling examples are all related to a Fabry–Perot resonator filled with the bulk n+-In0.53Ga0.47As as an active medium

Principles of Geocryology (Permafrost Studies). Part I, General Geocryology. Chapter X, Ground Water in Permafrost Areas. p. 328-364

Peer reviewed: NoNRC publication: Ye